Adaptive multi-resolution central-upwind schemes for systems of conservation laws

In this article, we develop an adaptive scheme for solving systems of hyperbolic conservation laws. In this scheme nonlinear shock and linear contact waves will be treated differently. The proposed scheme uses the Kurganov central-upwind scheme. Fourth-order non-oscillatory reconstruction is employed near shock only while the unlimited fifth-order reconstruction is used for smooth regions and linear contact waves. To distinguish between the smooth parts and discontinuities, we use an efficient adaptive multi-resolution technique. The advantages of the scheme are high resolution and computationally efficient since limiters are used only for shocks. Numerical experiments with one- and two-dimensional problems are presented which show the robustness of the proposed scheme.     

Raman Scattering at Resonant or Near-Resonant Conditions: A Generalized Short-Time Approximation

We investigate the dynamics of resonant Raman scattering in the course of the frequency de-tuning. The dephasing in the time domain makes the scattering fast when the photon energy is tuned from the absorption resonance. This makes frequency detuning to act as a cam-era shutter with a regulated scattering duration and provides a practical tool of controlling the scattering time in ordinary stationary measurements. The theory is applied to resonant Raman spectra of a couple of few-mode model systems and to trans-1,3,5-hexatriene and guanine-cytosine (G-C) Watson-Crick base pairs (DNA) molecules. Besides some particular physical effects, the regime of fast scattering leads to a simplification of the spectrum as well as to the scattering theory itself. Strong overtones appear in the Raman spectra when the photon frequency is tuned in the resonant region, while in the mode of fast scattering, the overtones are gradually quenched when the photon frequency is tuned more than one vibra-tional quantum below the first absorption resonance. The detuning from the resonant region thus leads to a strong purification of the Raman spectrum from the contamination by higher overtones and soft modes and purifies the spectrum also in terms of avoidance of dissociationand interfering fluorescence decay of the resonant state. This makes frequency detuning a very useful practical tool in the analysis of the resonant Raman spectra of complex systems and considerably improves the prospects for using the Raman effect for detection of foreign substances at ultra-low concentrations.     

The role of Co impurities and oxygen vacancies in the ferromagnetism of Co-doped SnO2: GGA and GGA+U studies

The electronic structure and ferromagnetic stability of Co-doped SnO₂ are studied using the first-principle density functional method within the generalized gradient approximation (GGA) and GGA+U schemes. The addition of effective U_Co transforms the ground state of Co-doped SnO₂ to insulating from half-metallic and the coupling between the nearest neighbor Co spins to weak antimagnetic from strong ferromagnetic. GGA+U_Co calculations show that the pure substitutional Co defects in SnO₂ cannot induce the ferromagnetism. Oxygen vacancies tend to locate near Co atoms. Their presence increases the magnetic moment of Co and induces the ferromagnetic coupling between two Co spins with large Co-Co distance. The calculated density of state and spin density distribution calculated by GGA+U_Co show that the long-range ferromagnetic coupling between two Co spins is mediated by spin-split impurity band induced by oxygen vacancies. More charge transfer from impurity to Co-3d states and larger spin split of Co-3d and impurity states induced by the addition of U_Co enhance the ferromagnetic stability of the system with oxygen vacancies. By applying a Coulomb U_O on O 2 s orbital, the band gap is corrected for all calculations and the conclusions derived from GGA+U_Co calculations are not changed by the correction of band gap.     

Quark dynamics, thermal QCD, and the gravity dual

We perform a holographic renormalization of the supergravity action and compute the stress tensor of the dual gauge theory incorporating the logarithmic running of the gauge coupling. From the stress tensor we obtain the shear viscosity and the entropy of the medium at temperature T, and investigate the ratio η/s.     

K2M(H2P2O7)2·2H2O (M = Ni,Cu, Zn): ortho­rhom­bic forms and Raman spectra

The crystal structures of three isotypic ortho­rhom­bic dihydrogendiphosphates, namely dipotassium copper(II)/nickel(II)/zinc(II) bis­(dihydrogendiphosphate) dihydrate, K₂M(H₂P₂O₇)₂·2H₂O (M = Cu, Ni and Zn), have been refined from single‐crystal data. The M²⁺ and K⁺ cations are located at sites of m symmetry, and the P atoms occupy general positions. These compounds also exist in triclinic forms with very similar structural features. The structures of both forms are compared, as well as the geometry of the MO₆ octa­hedron, which is considerably elongated towards the water mol­ecules for M = Ni and Cu. Such elongation has not been observed among the other representatives of the family. A Raman study of the whole series K₂M(H₂P₂O₇)₂·2H₂O (M = Mn, Co, Ni, Cu, Zn and Mg) is reported.     

Synthesis,cyclic voltammetry,and UV–Vis studies of ferrocene-dithiafulvalenes as anticipated electron-donor materials

Abstract  New ferrocenyl ketones were obtained as precursors of novel π-conjugated ferrocene-dithiafulvalene (Fc-DTF) and π-extended-ferrocenedithia-fulvalenes (π-exFc-DTF) as electron-donor conducting materials from ferrocene by a direct aroylation process using the Friedel–Crafts reaction. Novel Fc-DTF conjugates were synthesized using the Wittig–Horner reaction and their structures were determined. The redox behavior of the ferrocenyl carbonyl compounds Fc-DTF and Fc-π-exDTF was investigated in comparison to the parent ferrocene by means of cyclic voltammetry. A one-electron redox behavior was observed for carbonylferrocenes as one wave potential, while a two-electron process was observed as two oxidation waves for the conjugates. Introduction of electron-withdrawing groups led to increasing E _pa values and decreasing ΔE _p values. The UV–Vis spectra of some compounds were studied in comparison with ferrocene. The absorption spectra showed a red-shift with a slight increase in the absorption intensities. Graphical abstract        

Photobactericidal films from porphyrins grafted to alkylated cellulose - synthesis and bactericidal properties

Two series of porphyrinic cellulose laurate esters plastic films, where the photosensitizers are covalently linked to the cellulosic polymer have been synthesised by using a “one-pot, two-step” esterification reaction. The photosensitizers were first covalently bounded to the cellulosic polymer using either 4- or 11-carbon spacer arms. The porphyrinic plastic films were then obtained by a second esterification with lauric acid. The reaction was studied according to reaction time, temperature, lauric acid amount, pyridine playing the role proton trapping base. Para-toluenesulfonylchloride has been proved to be a powerful activating agent for this reaction. The drawback of the steric hindrance of the porphyrinic macrocycle towards cellulosic hydroxyl groups has been overcome by increasing the number of carbon of spacer arms from 4- to 11-carbons. The photobactericidal activity of these materials was evaluated against Gram positive and Gram negative strains bacteria. First results show that these new plastic films display photobactericidal activity for porphyrin grafting percentage higher than 0.16, whereas the non-porphyrinic control allowed full growth of bacteria. These materials could be an alternative in order to overcome the growing bacterial multiresistance to classical antibiotics.     

Reduction Kinetics of Thionine in Aerobic Condition with D-Galactose

Reduction kinetics of thionine (Th) with D-galactose (RH) was observed on a UV/Visible 1601 Shimadzu spectrophotometer at λmax 599 nm. The results showed that the initially slow reduction kinetics got enhanced and proceeded to completion within a few minutes. A pseudo first order kinetics was observed when influence of different parameters like concentration of dye and reductant, ionic strength and temperature was investigated. A significant shift in wave length from 599 to 517 nm was observed at alkaline pH whereas addition of a small amount of acid caused a shift in equilibrium. This resulted in the generation of oxidized form of thionine which was pragmatic in the presence of atmospheric oxygen. Change in ionic strength at elevated temperature lied to decrease in the rate constant. Thermodynamics activation parameters like Ea reflects a high amount of energy required for reduction of Th with RH whereas entropy of activation (∆S!) and free energy of activation (∆G!) show the highly solvated states of transient complex which was less disorderly arranged than the oxidized form of dye. A mechanism consistent with above findings has been discussed in the relevant section of paper.     

The Carroll and Chang conjecture of equal Indscal components when Candecomp/Parafac gives perfect fit

The Candecomp/Parafac algorithm approximates a set of matrices ${\mathbf{X}}_1\text{,}\dots \text{,}{\mathbf{X}}_I$ by products of the form ${\mathbf{AC}}_i{\mathbf{B}}^{\prime }$, with ${\mathbf{C}}_i$ diagonal, $i=1\text{,}\dots \text{,}I$. Carroll and Chang have conjectured that, when the matrices are symmetric, the resulting $\mathbf{A}$ and $\mathbf{B}$ will be column wise proportional. For cases of perfect fit, Ten Berge et al. have shown that the conjecture holds true in a variety of cases, but may fail when there is no unique solution. In such cases, obtaining proportionality by changing (part of) the solution seems possible. The present paper extends and further clarifies their results. In particular, where Ten Berge et al. solved all $I\times 2\times 2$ cases, now all $I\times 3\times 3$ cases, and also the $I\times 4\times 4$ cases for $I=2\text{,}8$, and 9 are clarified. In a number of cases, $\mathbf{A}$ and $\mathbf{B}$ necessarily have column wise proportionality when Candecomp/Parafac is run to convergence. In other cases, proportionality can be obtained by using specific methods. No cases were found that seem to resist proportionality.